Having sketched the concept of a self-referential formalization and de-formalization as a plausible explanation of the possibility of the significant proposition, we must now ask why Wittgenstein declares a theory of sense to be an illegitimate "confusion of formal concepts with concepts proper" (TLP 4.126)⁴ and thereby impossible.

The difficulty in explicating a language-action game lies in the fact that both the explication itself and the explicated language-action game become problematic with regard to their self-referentiality. On the one hand, the explicating propositions would have to be self-referential with respect to their system; on the other hand, the language-game to be explicated must be understood and presented as another, foreign self-referential system.⁵

There are basically two ways of describing a self-referential system. (1) One does so from the standpoint of another self-referential system. The describing system is then self-referential, but the described self-referential system degenerates into an other-referential one, with the consequence that problematic (namely foreign) evaluations (possibilities of sense) come into play, and an essential feature of the system (the autarky of the game) is lost. Or (2) the self-referential system is described by means of its own possibilities of sense. Both the describing and the described system would then be self-referential, but the description may become contradictory.

Since the Tractatus makes the strong presupposition of a universally valid language system, option (1), where at least two language systems are involved, is out of the question for it. And with regard to option (2), Wittgenstein points to the fact that a language system describing itself would be contradictory, the more so the more it claims to be universal. So Wittgenstein decides on a way out, option (3): the description of a self-referential system is nonsensical and superfluous. The self-referential character of the language system thereby remains secured, but a strongly universalist claim to the universal validity of the self-referential system in question is made in order to be able to assert the superfluousness of the description.

More precisely, this means that the autarkic-self-referential connection between possibility of sense and sense is declared stable and unsayable, i.e. as neither needing nor being able to be explained explicatively. What a theory of sense aims at can be replaced by "elucidation" by means of examples of application (TLP 3.263, 4.112), since possibilities of sense "show" themselves in the use of language (TLP 4.126 to 4.1274). In order to be able to assert (not only the nonsensicality but) also the superfluousness of a theory of sense, it is presupposed that there is one language system which is common to all language-games and to which everyone in principle has access, since it shows itself, or can be shown, in the use of language.

Possible and evidently absurd consequences of options (1) and (2), in which (under the assumption of a universal language system) formal concepts are confused with concepts proper, are used by Wittgenstein as indirect proofs in order to establish option (3) as the only viable one. The rejection of (1) and (2) draws in each case on one facet of self-referentiality: the benign and the malignant. Option (1) is abandoned because it dissolves benign self-referentiality, since the system is presented as other-referential.

This benign variant of self-referentiality can be reconstructed as the "autarky" of (the possibility of) sense. By this is meant that the dependence of a sense (of a de-formalized proposition) on a possibility of sense (of a formalized proposition) must be self-contained, i.e. must not be relativized by any external conditions, at least for the situation of the communicative propositional act. That is, meaning and understanding are limited by the horizon of the possibilities of a proposition's sense available at any given time, and in this respect they are self-referential and autarkic.

Option (1), however, would lead to one language system being described by another, and thus disturbed in its autarky: in principle, the describing system could in turn be described from the perspective of another, and so on. The sense of a proposition, which would be secured by the autarky of the language system, thereby becomes open and uncertain. The resulting infinite regress from language system to language system would have the consequence that no proposition would be significant in any communicative situation, since the possibilities of sense supporting it could be questioned permanently.⁶ An end would be in sight, on the other hand, only if one language system were singled out and not subjected to further thematization: the notorious petitio principii.

Option (2), by contrast, must be abandoned because it practises malignant self-referentiality. This can be reconstructed as the self-reference, leading to contradictions, of a fundamentalist theory of sense, one that explicates language as one language system. The same self-reference that makes sense, and thus reflection on (possibilities of) sense, possible causes every theory of sense to fail that aims to formulate possibilities of sense as conditions of the possibility of all sense, i.e. as the only possible language system. Benign self-reference turns into malignant self-reference because the explication of this language system would at the same time, on the one hand, reflect (formalize) the sense possible in this language system and, on the other hand, also be contained in this language system and have to actualize (de-formalize) its possibilities of sense.⁷

The consequences of this malignant self-reference can be twofold. On the one hand, the goal of the theory of sense becomes unattainable when the theory of sense degenerates into a self-perpetuating regress of explication in which, in principle, nothing new comes to light. A possibility of sense (a formal concept) that is established as a condition of a proposition "p" can also be established for the proposition that establishes this, and so on. The effect is that the certainty of the sense of "p" that must be presupposed for communicative use loses its foundation: a restless search for foundations within itself. On the other hand, the goal of the theory of sense becomes just as unattainable when it degenerates into a self-perpetuating regress of negation. A possibility of sense established as a condition of a proposition "p" must not hold for the theory-of-sense (meta-)proposition that makes the relevant statement about the proposition "p", but must nevertheless be applied (because within the system there is no other possibility of sense). So the possibility of sense in question is a condition of the possibility of this meta-proposition if and only if it is not. To illustrate with the classic example of Russell's paradox: "class", as a formal property of all expressions functioning as classes, is defined in a theory-of-sense (meta-)proposition as follows: "'Class' is the class of all classes that do not contain themselves". "Class" would thus be a condition of the possibility of this proposition (for the proposition applies this possibility of sense) if and only if it were not (for the application of this possibility contradicts its definition).⁸

After this reductio ad absurdum, a theory of sense that postulates that one language system is to serve as the universal foundation of language must be declared nonsensical and superfluous. The thesis of the superfluousness of a theory of sense (the necessity of silence), however, cannot simply be refuted by pointing to the impossibility of a single universal language system: there is also a positive aspect to the superfluousness of a theory of sense. For in the practice of linguistic communication, the validity of a language system must indeed be presupposed, at least for the communicative situation in question, so that the language-game functions. For as long as it functions, a theory-of-sense explication of it must therefore be superfluous.⁹

On the one hand, Wittgenstein stands in the tradition of transcendental philosophy, since he takes as his starting point the (transcendental) dependence of the proposition on conditions of the possibility of its sense. In this respect he is unshakeable, since without the assumption of this dependence the significance of a proposition could not be explained. On the other hand, he seems to undermine the programme of transcendental philosophy by demonstrating that the universalization of one language system into a super-language system entails the impossibility of propositions about the conditions of possibility.

When some interpreters of the Tractatus reject a transcendental-philosophical reading of it, they mostly cite the unsayability of the theory of sense: "Logic is transcendental" (TLP 6.13) because it is unsayable (TLP 6.421), whereas transcendental philosophy claims to be quite sayable by means of so-called synthetic a priori propositions. This objection can be turned around, however, insofar as it is precisely Wittgenstein who alludes to a contradiction within transcendental philosophy. If it is asserted that there is a transcendental dependence between a proposition (or, put epistemologically, a cognition) and conditions of possibility, it is presupposed that the proposition is significant. If it is significant, the explication of its conditions of possibility is relatively superfluous; seen in this way, a theory of sense too would be relatively superfluous. If it is further presupposed that the proposition is significant because the conditions of its possibility are universally valid (i.e. hold for all propositions), then a transcendental-philosophical explication of these conditions of possibility is absolutely superfluous and nonsensical, since it itself falls outside the language system presupposed as universally valid. According to the Tractatus, the claim of transcendental philosophy to formulate the conditions of the possibility of all propositions must be cured by recourse to linguistic practice, which for the time being manages without transcendental philosophy.